Signal Integrity Testing With a Vector Network Analyzer
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The document provides an introduction to vector network analysis. It discusses key topics like transmission lines, S-parameters, network analyzer architecture, calibration techniques, and common measurements. Vector network analyzers are used to characterize two-port devices by measuring the amplitude and phase of signals transmitted and reflected within the device. Calibration is necessary to remove systematic measurement errors and allow accurate determination of S-parameters.
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Signal Integrity Testing With a Vector Network Analyzer
- 1. Vector Network Analysis Introduction and Fundamentals
- 2. Agenda • Introduction • Transmission Lines • S-Parameters • Network Analyzer Architecture • Calibration • Other Measurements Fundamentals of Vector Network Analysis 2
- 3. Rohde & Schwarz 50 Years of Innovation in Network Analysis 1950s: World’s First VNA Z-g-Diagraph S-Parameter Analyzer 300 – 2400 MHz 1970s: ZPV Vector Analyzer ZPV-Z5 Test Set SWP Signal Generator PCA5 Process Controller 1990s: ZVM / ZVK / ZVR / ZVC World’s First Fundamental Mixing Automatic VNA’s 9kHz – 40GHz Recent R&S Innovations • First Embedding/De-embedding (R&S Patent) • First Multisource Network Analyzer (ZVB) • First True Differential Capability (ZVA) • First One-Box VNA Supporting Hot S22 (ZVA) • First VNA Supporting TOI Meas. (ZVA) • First Two-Tone Frequency Converter Group Delay (ZVA) 2000s: ZVA / ZVB / ZVT High-Speed Multi-Port VNA’s 300kHz – 500GHz Fundamentals of Vector Network Analysis 3
- 4. Spectrum Analyzers vs. Network Analyzers Measures Signals Measures Devices Spectrum Analyzers: Network Analyzers: • Measure signal amplitude characteristics, carrier level, sidebands, harmonics.. • Measure components, devices, circuits, subassemblies • Can demodulate (+ measure) complex signals • Contains sources and receivers • Spec Ans are receivers only (single channel) • Display ratioed amplitude and phase (frequency, power or time sweeps) • Can be used for scalar component test (no phase) with tracking gen. or external source Fundamentals of Vector Network Analysis • Offers advanced error correction. 4
- 5. What Devices do Network Analyzers Test? Filters RF Switches Couplers Cables Amplifiers Antennas Isolators Mixers … Most 2 (or more) port devices (and some 1 port devices) Fundamentals of Vector Network Analysis 5
- 6. Optical Analogy to RF Transmission • Network analyzers measure transmitted and reflected signals relative to the incident signal • Scalar analyzers measure magnitude only, vector analyzers measure magnitude and phase of these signals Incident Transmitted Optical Reflected DUT RF Fundamentals of Vector Network Analysis 6
- 7. Agenda • Introduction • Transmission Lines • S-Parameters • Network Analyzer Architecture • Calibration • Other Measurements Fundamentals of Vector Network Analysis 7
- 8. Transmission Lines Coax Cable Parallel Lines Microstrip Line Waveguide Fundamentals of Vector Network Analysis 8
- 9. Transmission Line Terminated with Short, Open Standing Wave (sum of incident and reflected waves) Zs = Zo V inc Vrefl OPEN: In-phase (0o) SHORT: Out-of-phase (180o) A transmission line terminated in a short or open reflects all power back to source Fundamentals of Vector Network Analysis 9
- 10. Transmission Line Terminated with Zo Zs = Zo Zo = characteristic impedance of transmission line Zo V inc Vrefl = 0 (all the incident power is absorbed in the load) A transmission line terminated in Zo behaves like an infinitely long transmission line Fundamentals of Vector Network Analysis 10
- 11. Transmission Line Terminated with 25Ω Standing Wave (sum of incident and reflected waves) Zs = Zo ZL = 25 Ω V inc Vrefl Standing wave pattern does not go to zero as with short or open Fundamentals of Vector Network Analysis 11
- 12. Agenda • Introduction • Transmission Lines • S-Parameters • Network Analyzer Architecture • Calibration • Other Measurements Fundamentals of Vector Network Analysis 12
- 13. High-Frequency Device Characterization Port 1 Port 2 Incident (“a1” receiver) Transmitted (“b2” receiver) Reflected (“b1” receiver) TRANSMISSION REFLECTION Reflected Incident = SWR S-Parameters S11, S22 Reflection Coefficient Γ, ρ b1 Transmitted a1 Incident Return Loss Impedance, Admittance R+jX, G+jB = b2 a1 Group Delay Gain / Loss Fundamentals of Vector Network Analysis S-Parameters S21, S12 Transmission Coefficient Τ,τ 13 Insertion Phase
- 14. S-Parameters • Basic DUT quantities measured by a VNA • Describe how DUT modifies a signal incident on any port Pin Pout Pin-refl Prev-refl • S11 (b1/a1) – Forward reflection coefficient (input match, return loss, VSWR) • S21 (b2/a1) – Forward transmission coefficient (gain or loss) • S12 (b1/a2) – Reverse transmission coefficient (reverse isolation) • S22 (b2/a2) – Reverse reflection coefficient (output match, return loss, VSWR) Fundamentals of Vector Network Analysis 14 Prev
- 15. Smith Chart • Published by Phillip H. Smith of Bell Labs in 1939 • Any impedance (resistive or reactive) can be plotted on a Smith chart • Used extensively in impedance matching Inductive Capacitive Short Fundamentals of Vector Network Analysis Match 15 Open
- 16. Reflection Parameters • Return Loss, VSWR, Impedance, and Scalar Reflection Coefficient are calculated from measured Vector Reflection Coefficient (Γ) Reflection (Γ) = V reflected Coefficient V incident ρ=Γ No reflection (ZL = Z0) 0 ∞ dB 1 VSWR = = ρ∠ Φ = Vmax 1 + ρ = Vmin 1 − ρ ZL − Z0 ZL + Z0 Return Loss = −20 log( ρ ) Full reflection (ZL = open, short) ρ 1 RL 0 dB ∞ VSWR Fundamentals of Vector Network Analysis 16
- 17. Criteria for Distortionless Transmission Linear phase over bandwidth of interest Constant amplitude over bandwidth of interest Phase Magnitude Frequency Frequency Distortion is indicated by: • Deviation from constant amplitude • Deviation from linear phase (or stated another way...) • Non-constant group delay Fundamentals of Vector Network Analysis 17
- 18. Distortion from Magnitude Variation vs. Frequency F(t) = sin ω t + 1/3 sin 3ω t + 1/5 sin 5ωt Time Time Magnitude Linear Network Frequency Frequency Fundamentals of Vector Network Analysis Frequency 18
- 19. Distortion from Non-Linear Phase F(t) = sin ω t + 1/3 sin 3ω t + 1/5 sin 5ωt Linear Network Time Magnitude Time 0° Frequency Frequency Frequency -180° -360° Fundamentals of Vector Network Analysis 19
- 20. Group Delay Frequency ω tg Group delay ripple ∆ω Phase to φ ∆φ Average delay Deviation from linear phase Frequency Group Delay = − dϕ − 1 dφ = * dω 360° df ϕ in radians ω in radians/sec φ in degrees VNAs calculate group delay from phase measurement across frequency Group-delay ripple indicates phase distortion (deviation from linear phase) Average delay indicates electrical length of DUT f in Hertz (ω = 2πf ) Aperture of group delay measurement is very important Fundamentals of Vector Network Analysis 20
- 21. Agenda • Introduction • Transmission Lines • S-Parameters • Network Analyzer Architecture • Calibration • Other Measurements Fundamentals of Vector Network Analysis 21
- 22. Scalar Network Analysis • Basic scalar analyzer can be a signal generator and a power meter LAN / GPIB LAN / GPIB Signal Generator Power Meter Fundamentals of Vector Network Analysis 22
- 23. Scalar Network Analysis • Basic scalar analyzer can be a spectrum analyzer with a tracking generator Spectrum Analyzer Fundamentals of Vector Network Analysis 23
- 24. Generic VNA Block Diagram b1 b2 a1 a2 Port 1 Fundamentals of Vector Network Analysis Port 2 24
- 25. ZVA 4-Port Test Set • Four Ports • Two Sources • All ports can source signals simultaneously • 8 Receivers • Modern calibration techniques • Some older VNAs shared receivers and could not do a TRL type calibration Fundamentals of Vector Network Analysis 25
- 26. ZVA 2-Port Block Diagram • Direct Receiver/Generator Access option • Used for high power devices, mixers, pulsed Measurements, etc. Fundamentals of Vector Network Analysis 26
- 27. Directional Coupler (Reflectometer) Directivity • Directivity is a measure of how well a coupler can separate signals moving in opposite directions • A termination at the test port should result in no signal at the b receiver • The difference between the coupled signal and the leakage signal is the directivity of the coupler (typical values: 15-25dB) b a (undesired leakage signal) (desired reflected signal) Test port Directional Coupler Fundamentals of Vector Network Analysis 27
- 28. Agenda • Introduction • Transmission Lines • S-Parameters • Network Analyzer Architecture • Calibration • Other Measurements Fundamentals of Vector Network Analysis 28
- 29. Measurement Errors Drift Errors • Caused by changes in environment after calibration (temperature, humidity) • Minimized by controlling test environment Random Errors • Caused by instrument noise, switch and connector repeatability • Not repeatable • Minimized by high quality equipment and good measurement practices DUT cannot be removed – only minimized Systematic Errors • Due to non-ideal components in the VNA and test setup • Assumed to be repeatable • Calibration is used to correct for these errors • Residual error limited by quality of calibration standards Fundamentals of Vector Network Analysis removed (nearly) with calibration 29
- 30. Systematic Measurement Errors Frequency Response • Reflection Tracking • Transmission Tracking Directivity a1 Crosstalk b2 b1 DUT Port 1 Source 6 forward and 6 reverse error terms yields 12 error terms for a 2 port device Fundamentals of Vector Network Analysis Source Mismatch Load Mismatch 30
- 31. Transmission Measurement Errors a1 a'1 T'1 Γ1 b2 DUT b1 a2 T2 Γ2 b'2 ETT ER1 ER2 ER3 EX Fundamentals of Vector Network Analysis 1. Forward Transmission Loss 2. Mismatch-reflections DUT / Port 1 3. Mismatch-reflections DUT / Port 2 4.Multiport mismatch-reflections 5. Crosstalk 31
- 32. Types of Error Correction Response (normalization) simple to perform only corrects for tracking errors stores reference trace in memory, then does data divided by memory thru Vector requires more standards requires an analyzer that can measure phase accounts for all major sources of systematic error SHORT S11 a thru OPEN S 11 m Fundamentals of Vector Network Analysis MATCH 32
- 33. Vector Error Correction Process of characterizing systematic error terms Measure known standards Remove effects from subsequent measurements 1-port calibration (reflection measurements) Only 3 systematic error terms measured Directivity, source match, and reflection tracking Full 2-port calibration (reflection and transmission measurements) 10 systematic error terms measured (crosstalk assumed to be zero) Usually requires 7 measurements on four known standards (TOSM) Thru need not be characterized (unknown thru calibration) Standards defined in cal kit definition file Network analyzer contains standard cal kit definitions CAL KIT DEFINITION MUST MATCH ACTUAL CAL KIT USED! User-built standards must be characterized and entered into user cal kit Fundamentals of Vector Network Analysis 33
- 34. Calibration Kits Mechanical and Electronic Type N 3.5mm 3.5mm w/sliding matches Type N Calibration Unit Connects to VNA via USB Fundamentals of Vector Network Analysis 34
- 35. Mechanical Calibration Types and Standards Uncorrected Response 1-Port Full 2-Port SHORT DUT DUT Easy to perform Use when highest accuracy is not required Removes frequency response error One Path – Two Port Combines response and 1-port Corrects source match for transmission measurements DUT MATC H thru For reflection measurements Need good termination for high accuracy with two-port devices Removes these errors: Directivity Source Match Reflection Tracking Fundamentals of Vector Network Analysis OPEN MATC H MATC H SHORT OPEN OPEN thru Convenient Generally not accurate, but can be useful for first-cut measurements No errors removed SHORT DUT Highest accuracy Removes these errors: Directivity Source & Load Match Reflection tracking Transmission Tracking 35
- 36. Automatic Calibration Units • • • • • Automatically performs a full calibration on all connected ports Connects to VNA via USB Equivalent to TOSM mechanical calibration Available in 2, 4 and 8 Port versions User definable port configurations Fundamentals of Vector Network Analysis 36
- 37. Improvement from a One-Port Calibration Measurement of match at the end of a 2ft cable uncalibrated 1-port cal Fundamentals of Vector Network Analysis 37
- 38. Two-Port Error Correction Each corrected S-parameter is a function of all four measured S-parameters VNA must make forward and reverse sweep to update any one S-parameter Forward Model EX Port 1 S11a = S S S − ED − ED ' − E X S12 m − E X ' ( 11m )(1 + 22m E S ' ) − E L ( 21m )( ) E RT E RT ' E TT E TT ' S S S − E D' − ED ' − E X S12 m − E X ' (1 + 11m E S )(1 + 22 m E S ' ) − E L ' E L ( 21m )( ) E RT E RT ' E TT ETT ' S21m − E X S22 m − E D ' )(1 + ( E S '− E L )) E TT E RT ' S S S − ED − ED' − E X S12 m − E X ' (1 + 11m E S )(1 + 22m E S ' ) − E L ' E L ( 21m )( ) E RT E RT ' E TT ETT ' a1 b1 ( S21a = S12 a = S S − EX ' − ED ( 12m )(1 + 11m ( E S − E L ' )) E TT ' E RT S S S − ED − ED' − E X S12m − E X ' (1 + 11m E S )(1 + 22m E S ' ) − E L ' E L ( 21m )( ) E RT E RT ' E TT E TT ' S22a = S 22m − E D ' S11m − E D S 21m − E X S12m − E X ' ( )( 1 + ES ) − E L ' ( )( ) E RT ' E RT E TT E TT ' S S S − ED − ED' − E X S12m − E X ' (1 + 11m E S )(1 + 22m E S ' ) − E L ' E L ( 21m )( ) E RT E RT ' E TT ETT ' S11A S22 Port 1 Port 2 S21 E L' b1 A EL b2 a2 A Reverse Model a1 ETT S 12 E RT E TT' Fundamentals of Vector Network Analysis S 21A ES ED Port 2 S11 A S22 A A E RT' E S' ED' b2 a2 S12 A EX' ED = fwd directivity ES = fwd source match ERT = fwd reflection tracking ED' = rev directivity E S' = rev source match E RT' = rev reflection tracking 38 EL = fwd load match ETT = fwd transmission tracking EX = fwd isolation EL' = rev load match ETT' = rev transmission tracking EX' = rev isolation
- 39. Modifications to Calibration • Port Extensions or Offsets • Extends reference plane by mathematically adding ideal transmission line • Many VNA’s can automatically set extension length by making a reflection measurement when the line is terminated with an open or short • Some modern VNA’s can model loss into the extension • Embedding / De-embedding • More sophisticated than simple port extensions • Adds (embeds) or subtracts (de-embeds) an arbitrary network to the reference plane • Network can be modeled from various RLC networks or S-parameter data (.s2p format) • Examples: • Extract DUT measurements when embedded in a fixture with known Sparameters • Simulate adding a matching component or network to the input of a DUT Fundamentals of Vector Network Analysis 39
- 40. Agenda • Introduction • Transmission Lines • S-Parameters • Network Analyzer Architecture • Calibration • Other Measurements Fundamentals of Vector Network Analysis 40
- 41. Balanced Devices Ideal device responds to differential input signals and rejects common-mode input signals Differential-mode signal Balanced to single-ended Common-mode signal (EMI or ground noise) Differential-mode signal Fully balanced Common-mode signal (EMI or ground noise) Fundamentals of Vector Network Analysis 41
- 42. Balanced Device Measurement • Most VNA’s have a “Virtual Differential” mode • In “Virtual Differential” mode stimulus is applied to one port at a time and superposition is used to calculate differential results • ZVA provides an optional “True Differential” mode • In “True Differential” mode the dual sources are used to apply differential in-phase and out-of-phase stimulus to the DUT Fundamentals of Vector Network Analysis 42
- 43. Mixer Measurement (scalar) • Use second source as LO • Use additional (3rd) source for mixer TOI measurement LAN / GPIB Fundamentals of Vector Network Analysis 43
- 44. Mixer Delay – No LO Access Two-Tone Technique • • • • • Uses phase coherent internal sources ZVA receivers can measure two tones simultaneously Tolerates large LO drift Works very well with DUTs containing multiple conversion stages No mismatch error correction – must use pads Fundamentals of Vector Network Analysis 44
- 45. Vector Mixer Measurements • Traditionally difficult measurement for VNA • Modern VNA architecture and calibration techniques full frequency converter characterization – S11, S22 and absolute phase and delay LO from ZVA or external Source RF IF LO LO Splitter RF IF LO IF LO MUT Measurement and Calibration plane Fundamentals of Vector Network Analysis RF 45 LP-Filter
- 46. Power Sweep – Gain Compression Output Power (dBm) Saturated output power Compression region Linear region (slope = small-signal gain) Input Power (dBm) Fundamentals of Vector Network Analysis 46
- 47. Power Sweep - Gain Compression 1 dB Compression Point: output (or input) power resulting in 1dB drop in gain Fundamentals of Vector Network Analysis 47
- 48. TOI Measurement Fixed TOI Two sources set to fixed frequencies while receiver sweeps (like spectrum analyzer measurement) Swept TOI Sources sweep with fixed offset while receiver track at the IM3 frequency (very difficult with spectrum analyzer) Fundamentals of Vector Network Analysis 48
- 49. Hot S22 Measurement • Normal (cold) S22 is measured with no signal on input of DUT • Hot S22 is measured with DUT (amp) in active state • Signal from Port 1 puts amplifier in operating mode (f2) • S22 is measured at different frequency (f1) • Measures amplifier under realistic operating conditions ROHDE&SCHWARZ ZVA 24 VECTOR NETWORK ANALYZER 10 MHz … 24 GHz 3 1 4 2 f1 f2 Fundamentals of Vector Network Analysis 49 f2
- 50. DC Current & Power Added Efficiency • Makes use of ZVA‘s built-in voltmeters DCmeas +/-1V DCmeas +/-10V U= P3 P1 P4 P1 Fundamentals of Vector Network Analysis P2 P= P2 Rmeas 50
- 51. Amplifier Measurements Many results on one display • S11 and S21 • Hot and Cold S22 • DC Current vs. Frequency • 1dB Compression Point at Low, Mid, and High Freqs • DC Current vs. Input Power • 2nd Harmonic Suppression vs. Frequency • 2nd Harmonic Suppression vs. Input Power • TOI Fundamentals of Vector Network Analysis 51
- 52. Programming emulation of some VNA‘s you may have heard of... Fundamentals of Vector Network Analysis 52
- 53. 40 GH z 50 GH z 67 GH z 80 GH z 50 0G Hz Hz 24 G Hz 20 G Hz 14 G Hz 8G Hz Hz 6G 3G 4G Hz Hz 10 M 30 0k Hz ZVA / ZVT with External Converters ZV-Zxxx ZVA80 [2 & 4 ports, 1.00mm(m)] ZVA67 [2 & 4 ports, 1.85mm(m)] Top Class ZVA50 [2 & 4 ports, 2.4mm(m)] ZVA40 [2 & 4 ports, , 2.92mm(m), or 2.4mm(m)] ZVA24 [2 & 4 ports , 3.5mm(m)] ZVA8 [2 & 4 ports, N(f)] ZVT20 [2 to 6 ports , 3.5mm(m)] 150 kHz (unspecified) 9 kH z R&S Network Analyzer Family Multiport & Production ZVT8 [2 to 8 ports, N(f)] ZVB20 [2 & 4 ports , 3.5mm(m)] ZVB14 [2 & 4 ports, 3.5mm(m)] ZVB8 [2 & 4 ports, N(f)] ZVB4 [2 & 4 ports, N(f)] ZVL13 [2 ports, N(f)] General Purpose Compact & Flexible ZVL6 [2 ports, N(f)] ZVL3 [2 ports, N(f)] Fundamentals of Vector Network Analysis 53
- 54. Fundamentals of Vector Network Analysis 54
Editor's Notes
- Network analyzer is used to characterize devices such as mixers, amplifiers, attenuators etc. Network analyzer can provide vector error corrected measurements on S parameters Commonly used to measure gain, VSWR, etc. The network analyzer has it’s own synthesizer…hense it is used to measure known signals…i.e. the synthesizer supplies the signal used to measure common S parameters. The spectrum analyzer as mentioned previously is used to measure unknown signals…i.e. signals it did not create. The one exception to this is when using a tracking generator. It can only do scalar calibration
- Slide 3 Here are some examples of the types of devices that you can test with network analyzers. They include both passive and active devices (and some that have attributes of both). Many of these devices need to be characterized for both linear and nonlinear behavior. It is not possible to completely characterize all of these devices with just one piece of test equipment. The next slide shows a model covering the wide range of measurements necessary for complete linear and nonlinear characterization of devices. This model requires a variety of stimulus and response tools. It takes a large range of test equipment to accomplish all of the measurements shown on this chart. Some instruments are optimized for one test only (like bit-error rate), while others, like network analyzers, are much more general-purpose in nature. Network analyzers can measure both linear and nonlinear behavior of devices, although the measurement techniques are different (frequency versus power sweeps for example). This module focuses on swept-frequency and swept-power measurements made with network analyzers
- Slide 5 One of the most fundamental concepts of high-frequency network analysis involves incident, reflected and transmitted waves traveling along transmission lines. It is helpful to think of traveling waves along a transmission line in terms of a lightwave analogy. We can imagine incident light striking some optical component like a clear lens. Some of the light is reflected off the surface of the lens, but most of the light continues on through the lens. If the lens were made of some lossy material, then a portion of the light could be absorbed within the lens. If the lens had mirrored surfaces, then most of the light would be reflected and little or none would be transmitted through the lens. This concept is valid for RF signals as well, except the electromagnetic energy is in the RF range instead of the optical range, and our components and circuits are electrical devices and networks instead of lenses and mirrors. Network analysis is concerned with the accurate measurement of the ratios of the reflected signal to the incident signal, and the transmitted signal to the incident signal.
- Twisted pair not used in RF and microwave Waveguide is lowest loss but narrow band Also used for higher frequencies i.e. mm wave
- Slide 13 Next, let's terminate our line in a short circuit. Since purely reactive elements cannot dissipate any power, and there is nowhere else for the energy to go, a reflected wave is launched back down the line toward the source. For Ohm's law to be satisfied (no voltage across the short), this reflected wave must be equal in voltage magnitude to the incident wave, and be 180o out of phase with it. This satisfies the condition that the total voltage must equal zero at the plane of the short circuit. Our reflected and incident voltage (and current) waves will be identical in magnitude but traveling in the opposite direction. Now let us leave our line open. This time, Ohm's law tells us that the open can support no current. Therefore, our reflected current wave must be 180o out of phase with respect to the incident wave (the voltage wave will be in phase with the incident wave). This guarantees that current at the open will be zero. Again, our reflected and incident current (and voltage) waves will be identical in magnitude, but traveling in the opposite direction. For both the short and open cases, a standing-wave pattern will be set up on the transmission line. The valleys will be at zero and the peaks at twice the incident voltage level. The peaks and valleys of the short and open will be shifted in position along the line with respect to each other, in order to satisfy Ohm's law as described above.
- Slide 12 Let's review what happens when transmission lines are terminated in various impedances, starting with a Zo load. Since a transmission line terminated in its characteristic impedance results in maximum transfer of power to the load, there is no reflected signal. This result is the same as if the transmission line was infinitely long. If we were to look at the envelope of the RF signal versus distance along the transmission line, it would be constant (no standing-wave pattern). This is because there is energy flowing in one direction only.
- Slide 14 Finally, let's terminate our line with a 25 resistor (an impedance between the full reflection of an open or short circuit and the perfect termination of a 50 load). Some (but not all) of our incident energy will be absorbed in the load, and some will be reflected back towards the source. We will find that our reflected voltage wave will have an amplitude 1/3 that of the incident wave, and that the two waves will be 180o out of phase at the load. The phase relationship between the incident and reflected waves will change as a function of distance along the transmission line from the load. The valleys of the standing-wave pattern will no longer be zero, and the peak will be less than that of the short/open case. The significance of standing waves should not go unnoticed. Ohm's law tells us the complex relationship between the incident and reflected signals at the load. Assuming a 50-ohm source, the voltage across a 25-ohm load resistor will be two thirds of the voltage across a 50-ohm load. Hence, the voltage of the reflected signal is one third the voltage of the incident signal and is 180o out of phase with it. However, as we move away from the load toward the source, we find that the phase between the incident and reflected signals changes! The vector sum of the two signals therefore also changes along the line, producing the standing wave pattern. The apparent impedance also changes along the line because the relative amplitude and phase of the incident and reflected waves at any given point uniquely determine the measured impedance. For example, if we made a measurement one quarter wavelength away from the 25-ohm load, the results would indicate a 100-ohm load. The standing wave pattern repeats every half wavelength, as does the apparent impedance.
- Slide 15 Now that we fully understand the relationship of electromagnetic waves, we must also recognize the terms used to describe them. Common network analyzer terminology has the incident wave measured with the R (for reference) receiver. The reflected wave is measured with the A receiver and the transmitted wave is measured with the B receiver. With amplitude and phase information of these three waves, we can quantify the reflection and transmission characteristics of our device under test (DUT). Some of the common measured terms are scalar in nature (the phase part is ignored or not measured), while others are vector (both magnitude and phase are measured). For example, return loss is a scalar measurement of reflection, while impedance results from a vector reflection measurement. Some, like group delay, are purely phase-related measurements. Ratioed reflection is often shown as A/R and ratioed transmission is often shown as B/R, relating to the measurement receivers used in the network analyzer
- Talk about A1 is incident A is source 1 is port 1 B1 is reflected wave at port 1 B is reflected 1 is port one Review defiinitions for Sparmeters at the bottom Different terms for the same thing i.e. s11, return loss, vswr etc.
- Reflection coefficient gamma(r) Magnitude of the reflection coefficient is rho Reflection Coefficient: shows what fraction of an incident signal is reflected when a source drives a load. Standing Wave Ratio (SWR): is the ratio of the maximum to minimum values of the "standing wave" pattern that is created when signals are reflected on a transmission line. This measurement can be taken using a "slotted line" apparatus that allows the user to measure the field strength in a transmission line at different distances along the line. Return Loss: shows the level of the reflected signal with respect to the incident signal in dB. The negative sign is dropped from the return loss value, so a large value for return loss indicates a small reflected signal. Example: a return loss of 26 dB is roughly equivalent to a reflection coefficient of 0.05.
- Slide 20 Now lets examine how linear networks can cause signal distortion. There are three criteria that must be satisfied for linear distortionless transmission. First, the amplitude (magnitude) response of the device or system must be flat over the bandwidth of interest. This means all frequencies within the bandwidth will be attenuated identically. Second, the phase response must be linear over the bandwidth of interest. And last, the device must exhibit a "minimum-phase response", which means that at 0 Hz (DC), there is 0o phase shift (0o n*180o is okay if we don't mind an inverted signal). How can magnitude and phase distortion occur? The following two examples will illustrate how both magnitude and phase responses can introduce linear signal distortion.
- Slide 21 Here is an example of a square wave (consisting of three sinusoids) applied to a bandpass filter. The filter imposes a non-uniform amplitude change to each frequency component. Even though no phase changes are introduced, the frequency components no longer sum to a square wave at the output. The square wave is now severely distorted, having become more sinusoidal in nature.
- Slide 22 Let's apply the same square wave to another filter. Here, the third harmonic undergoes a 180o phase shift, but the other components are not phase shifted. All the amplitudes of the three spectral components remain the same (filters which only affect the phase of signals are called allpass filters). The output is again distorted, appearing very impulsive this time.
- Slide 24 Another useful measure of phase distortion is group delay. Group delay is a measure of the transit time of a signal through the device under test, versus frequency. Group delay is calculated by differentiating the insertion-phase response of the DUT versus frequency. Another way to say this is that group delay is a measure of the slope of the transmission phase response. The linear portion of the phase response is converted to a constant value (representing the average signal-transit time) and deviations from linear phase are transformed into deviations from constant group delay. The variations in group delay cause signal distortion, just as deviations from linear phase cause distortion. Group delay is just another way to look at linear phase distortion. When specifying or measuring group delay, it is important to quantify the aperture in which the measurement is made. The aperture is defined as the frequency delta used in the differentiation process (the denominator in the group-delay formula). As we widen the aperture, trace noise is reduced but less group-delay resolution is available (we are essentially averaging the phase response over a wider window). As we make the aperture more narrow, trace noise increases but we have more measurement resolution.
- Free software to do basic scalar analysis available on website
- Free software to do basic scalar analysis available on website
- Slide 34 Here is a generalized block diagram of a network analyzer, showing the major signal-processing sections. In order to measure the incident, reflected and transmitted signal, four sections are required: Source for stimulus Signal-separation devices Receivers that downconvert and detect the signals Processor/display for calculating and reviewing the results We will briefly examine each of these sections. More detailed information about the signal separation devices and receiver section are in the appendix.
- With direct receiver access you have direct access to both sources and all 8 receivers
- Slide 34 Here is a generalized block diagram of a network analyzer, showing the major signal-processing sections. In order to measure the incident, reflected and transmitted signal, four sections are required: Source for stimulus Signal-separation devices Receivers that downconvert and detect the signals Processor/display for calculating and reviewing the results We will briefly examine each of these sections. More detailed information about the signal separation devices and receiver section are in the appendix.
- Slide 37 Unfortunately, real signal-separation devices are never perfect. For example, let's take a closer look at the actual performance of a 3-port directional coupler. Ideally, a signal traveling in the coupler's reverse direction will not appear at all at the coupled port. In reality, however, some energy does leak through to the coupled arm, as a result of finite isolation. One of the most important parameter for couplers is their directivity. Directivity is a measure of a coupler's ability to separate signals flowing in opposite directions within the coupler. It can be thought of as the dynamic range available for reflection measurements. Directivity can be defined as: Directivity (dB) = Isolation (dB) - Forward Coupling Factor (dB) - Loss (through-arm) (dB) The appendix contains a slide showing how adding attenuation to the ports of a coupler can affect the effective directivity of a system (such as a network analyzer) that uses a directional coupler. As we will see in the next slide, finite directivity adds error to our measured results.
- Slide 54 The two main types of error correction that can be done are response (normalization) corrections and vector corrections. Response calibration is simple to perform, but only corrects for a few of the twelve possible systematic error terms (the tracking terms). Response calibration is essentially a normalized measurement where a reference trace is stored in memory, and subsequent measurement data is divided by this memory trace. A more advanced form of response calibration is open/short averaging for reflection measurements using broadband diode detectors. In this case, two traces are averaged together to derive the reference trace. Vector-error correction requires an analyzer that can measure both magnitude and phase. It also requires measurements of more calibration standards. Vector-error correction can account for all the major sources of systematic error and can give very accurate measurements. Note that a response calibration can be performed on a vector network analyzer, in which case we store a complex (vector) reference trace in memory, so that we can display normalized magnitude or phase data. This is not the same as vector-error correction however (and not as accurate), because we are not measuring and removing the individual systematic errors, all of which are complex or vector quantities.
- Slide 55 Vector-error correction is the process of characterizing systematic error terms by measuring known calibration standards, and then removing the effects of these errors from subsequent measurements. One-port calibration is used for reflection measurements and can measure and remove three systematic error terms (directivity, source match, and reflection tracking). Full two-port calibration can be used for both reflection and transmission measurements, and all twelve systematic error terms are measured and removed. Two-port calibration usually requires twelve measurements on four known standards (short-open-load-through or SOLT). Some standards are measured multiple times (e.g., the through standard is usually measured four times). The standards themselves are defined in a cal-kit definition file, which is stored in the network analyzer. Agilent network analyzers contain all of the cal-kit definitions for our standard calibration kits. In order to make accurate measurements, the cal-kit definition MUST MATCH THE ACTUAL CALIBRATION KIT USED! If user-built calibration standards are used (during fixtured measurements for example), then the user must characterize the calibration standards and enter the information into a user cal-kit file. Sources of more information about this topic can be found in the appendix.
- Slide 55 Vector-error correction is the process of characterizing systematic error terms by measuring known calibration standards, and then removing the effects of these errors from subsequent measurements. One-port calibration is used for reflection measurements and can measure and remove three systematic error terms (directivity, source match, and reflection tracking). Full two-port calibration can be used for both reflection and transmission measurements, and all twelve systematic error terms are measured and removed. Two-port calibration usually requires twelve measurements on four known standards (short-open-load-through or SOLT). Some standards are measured multiple times (e.g., the through standard is usually measured four times). The standards themselves are defined in a cal-kit definition file, which is stored in the network analyzer. Agilent network analyzers contain all of the cal-kit definitions for our standard calibration kits. In order to make accurate measurements, the cal-kit definition MUST MATCH THE ACTUAL CALIBRATION KIT USED! If user-built calibration standards are used (during fixtured measurements for example), then the user must characterize the calibration standards and enter the information into a user cal-kit file. Sources of more information about this topic can be found in the appendix.
- Slide 60 A network analyzer can be used for uncorrected measurements, or with any one of a number of calibration choices, including response calibrations and one- or two-port vector calibrations. A summary of these calibrations is shown above. We will explore the measurement uncertainties associated with the various calibration types in this section.
- Slide 57 Shown here is a plot of reflection with and without one-port calibration. Without error correction, we see the classic ripple pattern caused by the systematic errors interfering with the measured signal. The error-corrected trace is much smoother and better represents the device's actual reflection performance.
- Slide 58 Two-port error correction is the most accurate form of error correction since it accounts for all of the majorsources of systematic error. The error model for a two-port device is shown above. Shown below are the equations to derive the actual device S-parameters from the measured S-parameters, once the systematic error terms have been characterized. Notice that each actual S-parameter is a function of all four measured S-parameters. The network analyzer must make a forward and reverse sweep to update any one S-parameter. Luckily, you don't need to know these equations to use network analyzers!!!
- Slide 104 Let's briefly review how balanced devices work. Ideally, a balanced device only responds to or generates differential-mode signals, which are defined as two signals that are 180o out of phase with one another. These devices do not respond to or generate in-phase signals, which are called common-mode signals. In the top example of a balanced-to-single-ended amplifier, we see that the amplifier is responding the differential input, but there is no output when common-mode or in-phase signals are present at the input of the amplifier. The lower example shows a fully balanced amplifier, which is both differential inputs and outputs. Again, the amplifier only responds to the differential input signals, and does not produce an output in response to the common-mode input. One of the main reasons that balanced circuits are desirable is because external signals that are radiated from an RF emitter show up at the terminals of the device as common mode, and are therefore rejected by the device. These interfering signals may be from other RF circuitry or from the harmonics of digital clocks or data. Balanced circuits also reject noise on the electrical ground, since the noise appears in phase to both input terminals, making it a common-mode signal.
- Slide 81 Many network analyzers have the ability to do power sweeps as well as frequency sweeps. Power sweeps help characterize the nonlinear performance of an amplifier. Shown above is a plot of an amplifier's output power versus input power at a single frequency. Amplifier gain at any particular power level is the slope of this curve. Notice that the amplifier has a linear region of operation where gain is constant and independent of power level. The gain in this region is commonly referred to as "small-signal gain". At some point as the input power is increased, the amplifier gain appears to decrease, and the amplifier is said to be in compression. Under this nonlinear condition, the amplifier output is no longer sinusoidal -- some of the output power is present in harmonics, rather than occurring only at the fundamental frequency. As input power is increased even more, the amplifier becomes saturated, and output power remains constant. At this point, the amplifier gain is essentially zero, since further increases in input power result in no change in output power. In some cases (such as with TWT amplifiers), output power actually decreases with further increases in input power after saturation, which means the amplifier has negative gain. Saturated output power can be read directly from the above plot. In order to measure the saturated output power of an amplifier, the network analyzer must be able to provide a power sweep with sufficient output power to drive the amplifier from its linear region into saturation. A preamp at the input of the amplifier under test may be necessary to achieve this.
- Slide 82 The most common measurement of amplifier compression is the 1-dB-compression point, defined here as the input power* which results in a 1-dB decrease in amplifier gain (referenced to the amplifier's small-signal gain). The easiest way to measure the 1-dB-compression point is to directly display normalized gain (B/R) from a power sweep. The flat part of the trace is the linear, small-signal region, and the curved part on the right side corresponds to compression caused by higher input power. As shown above, the 1-dB-compression point of the amplifier-under-test is 12.3 dBm, at a CW frequency of 902.7 MHz. It is often helpful to also know the output power corresponding to the 1-dB-compression point. Using the dual-channel feature found on most modern network analyzers, absolute power and normalized gain can be displayed simultaneously. Display markers can read out both the output power and the input power where 1-dB-compression occurs. Alternatively, the gain of the amplifier at the 1-dB-compression point can simply be added to the 1-dB-compression power to compute the corresponding output power. As seen above, the output power at the 1-dB-compression point is 12.3 dBm + 31.0 dB = 43.3 dBm. It should be noted that the power-sweep range needs to be large enough to ensure that the amplifier under test is driven from its linear region into compression. Modern network analyzers typically provide power sweeps with 15 to 25 dB of range, which is more than adequate for most amplifiers. It is also very important to sufficiently attenuate the output of high-power amplifiers to prevent damage to the network analyzer's receiver. * The 1-dB-compression point is sometimes defined as the output power resulting in a 1-dB decrease in amplifier gain (as opposed to the input power).